How to resolve the algorithm Primality by Wilson's theorem step by step in the Factor programming language

Published on 12 May 2024 09:40 PM
#Factor

How to resolve the algorithm Primality by Wilson's theorem step by step in the Factor programming language

Table of Contents

Problem Statement

Write a boolean function that tells whether a given integer is prime using Wilson's theorem. By Wilson's theorem, a number p is prime if and only if p divides (p - 1)! + 1. Remember that 1 and all non-positive integers are not prime.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Primality by Wilson's theorem step by step in the Factor programming language

Source code in the factor programming language

USING: formatting grouping io kernel lists lists.lazy math
math.factorials math.functions prettyprint sequences ;

: wilson ( n -- ? ) [ 1 - factorial 1 + ] [ divisor? ] bi ;
: prime? ( n -- ? ) dup 2 < [ drop f ] [ wilson ] if ;
: primes ( -- list ) 1 lfrom [ prime? ] lfilter ;

"n    prime?\n---  -----" print
{ 2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 }
[ dup prime? "%-3d  %u\n" printf ] each nl

"First 120 primes via Wilson's theorem:" print
120 primes ltake list>array 20 group simple-table. nl

"1000th through 1015th primes:" print
16 primes 999 [ cdr ] times ltake list>array
[ pprint bl ] each nl

You may also check:How to resolve the algorithm Hash join step by step in the Nim programming language
You may also check:How to resolve the algorithm Permutations step by step in the PowerShell programming language
You may also check:How to resolve the algorithm Mad Libs step by step in the Tcl programming language
You may also check:How to resolve the algorithm Count occurrences of a substring step by step in the Simula programming language
You may also check:How to resolve the algorithm Matrix multiplication step by step in the Scheme programming language